In a digital communication system, a signal is sent by a sender to a receiver via a transmission channel. The signal is modulated, which means that the characteristics of a carrier wave are varied so as to convey information (typically represented using binary symbols ‘0’ and ‘1’). In the case of a phase modulation, the useful information is transmitted by varying the phase of the signal to be transmitted. The aim of the receiver is to demodulate the signal, that is to say to detect the variations of the phase of the signal in reception. Continuous phase modulations (CPM) form a particular family of the phase modulations for which the variations of the phase of the signal are conducted continuously from one symbol to another. For other types of phase modulations, such as M-PSK (modulation with M phase states, PSK standing for “Phase Shift Keying”), major variations in the phase of the signal can be observed between two symbols. These broaden the spectrum, in other words, the band occupied by the signal. With regard to continuous phase modulations, because they induce a continuous variation of the phase of the signal, they make it possible to obtain good performance levels in terms of spectral efficiency.
GMSK “Gaussian Minimum Shift Keying” modulation is a modulation belonging to the family of continuous phase modulations. This has the property of using a Gaussian filter used to filter the data before modulating the carrier wave. The effect of this filter is to render the phase transitions from one symbol to another more progressive than, for example, for an MSK (“Minimum Shift Keying”) modulation. The characteristics of this modulation make it possible to effectively use the power amplifier on the sender side because the latter can work in a saturation area. These properties make GMSK modulation particularly suited to satellite transmissions. As an example, a future satellite navigation and data collection system will use this modulation coupled with a rate 1/2 convolutional encoder.
For a telecommunications system to function correctly, it is essential to synchronize the receiver on the received signal. In practice, if this is not the case, the reception performance levels will be degraded by notably increasing the bit error rate. Even if the sender and the receiver have their internal clocks synchronized on initialization of the communication, the situation may change over time. Taking the example of wireless telecommunications, when the sender and the receiver are in motion relative to one another, the Doppler effect introduces a frequency and time shift on the received signal. The loss of synchronization also has other causes, such as the imperfections of the oscillators used by the sender and the receiver. It is therefore necessary when designing a telecommunications system to consider this aspect and to use effective synchronization algorithms. One way of estimating the reliability of these algorithms is to compare their estimation performance levels with the Cramer-Rao limit. This limit indicates the greatest accuracy that can be obtained by an estimator.
The known synchronization methods for signals using a continuous phase modulation, such as the MSK or GMSK modulations, notably use these two types of methods.
The first method is called NDA (non data aided) and is derived from the method described by Rudi de Buda in his article “Coherent Demodulation of Frequency-Shift Keying With Low Deviation Ratio” (IEEE transactions on communications, June 1972). For example, the GMSK modulation with B.Ts=0.5, B.Ts being the product of the band of the signal and of the symbol period, can considered as a particular case of the FSK modulation at two frequencies F1 and F2. The method is based on the squaring of the modulated signal and can be used to find a ray at frequency 2*F1 and a ray at the frequency 2*F2. From these 2 rays, it is possible to find a carrier signal and a rate clock. The problem with this method is that, with a low Es/N0 ratio (ratio between the symbol energy and the power spectral density of reception noise) and because of the squaring, the phase noise is at a very high level which demands the use of phase-locked loops with a loop band reduced to a few Hertz, which is incompatible with the trend of the offset due to the Doppler effect in the case, for example, of a signal received by a satellite-borne receiver.
The second known method is to employ a pilot subcarrier or else a pilot sequence. The use of a subcarrier during the transmission of the data increases the complexity of the sender, and means that the sender can no longer function with saturation of its power amplifier. Because of this, for a given power supply power, there is less useful power available for the transmission of the data because of the presence of the subcarrier which detracts from this useful power and because of the necessary power back-off of the sender to generate the useful signal and the subcarrier without interfering intermodulations. The power back-off of a sender is the method which consists in employing its power amplifier with reduced input level, or backed off, to make it function in a quasi-linear region.